Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T14:50:28.262Z Has data issue: false hasContentIssue false
  • English
  • Français

Measuring Surface Topography by Scanning Electron Microscopy. II. Analysis of Three Estimators of Surface Roughness in Second Dimension and Third Dimension

Published online by Cambridge University Press:  09 December 2005

Rita Dominga Bonetto ,
Juan Luis Ladaga  and
Ezequiel Ponz
Rita Dominga Bonetto
Affiliation:
Centro de Investigación y Desarrollo en Ciencias Aplicadas Dr. Jorge J. Ronco (CINDECA) CONICET—UNLP, 47 No. 257-CC 59, 1900 La Plata, Argentina
Juan Luis Ladaga
Affiliation:
Facultad de Ingeniería de la Universidad Nacional de Buenos Aires, Departamento de Física—Laboratorio de Láser, Paseo Colón 850, Ciudad Autónoma de Buenos Aires, Argentina
Ezequiel Ponz
Affiliation:
Centro de Investigación y Desarrollo en Ciencias Aplicadas Dr. Jorge J. Ronco (CINDECA) CONICET—UNLP, 47 No. 257-CC 59, 1900 La Plata, Argentina
Get access

Abstract

Scanning electron microscopy (SEM) is widely used in surface studies and continuous efforts are carried out in the search of estimators of different surface characteristics. By using the variogram, we developed two of these estimators that were used to characterize the surface roughness from the SEM image texture. One of the estimators is related to the crossover between fractal region at low scale and the periodic region at high scale, whereas the other estimator characterizes the periodic region. In this work, a full study of these estimators and the fractal dimension in two dimensions (2D) and three dimensions (3D) was carried out for emery papers. We show that the obtained fractal dimension with only one image is good enough to characterize the roughness surface because its behavior is similar to those obtained with 3D height data. We show also that the estimator that indicates the crossover is related to the minimum cell size in 2D and to the average particle size in 3D. The other estimator has different values for the three studied emery papers in 2D but it does not have a clear meaning, and these values are similar for those studied samples in 3D. Nevertheless, it indicates the formation tendency of compound cells. The fractal dimension values from the variogram and from an area versus step log–log graph were studied with 3D data. Both methods yield different values corresponding to different information from the samples.

Keywords

dynamic programmingfractal dimensionsurface roughnessSEMstereomicroscopy
Type
MICROSCOPY TECHNIQUES
Information
Microscopy and Microanalysis , Volume 12 , Issue 2 , April 2006 , pp. 178 - 186
Copyright
© 2006 Microscopy Society of America

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., Peitgen, H.O., Dietmar, S., & Voss, R.F. (1988). The Science of Fractal Images, Peitgen, Heinz-Otto & Saupe, Dietmar (Eds.), pp. 67–69. New York: Springer-Verlag.
Bianchi, F.D. & Bonetto, R.D. (2001). FERImage: An interactive program for fractal dimension, dper and dmin calculation. Scanning 23, 193–197.Google Scholar
Bonetto, R.D., Forlerer, E., & Ladaga, J.L. (2002). Texture characterization of digital images which have a periodicity or a quasi-periodicity. Measure Sci Technol 13, 1458–1466.Google Scholar
Bonetto, R.D. & Ladaga, J.L. (1998). The variogram method for characterization of SEM images. Scanning 20, 457–463.Google Scholar
Dong, W.P., Sullivan, P.J., & Stout, K.J. (1994). Comprehensive study of parameters for characterizing third-dimensional surface topography. III: Parameters for characterizing amplitude and some functional properties. Wear 178, 29–43.Google Scholar
Einstein, A. (1905). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Phys 322, 549–560. [For an English translation, see A. Einstein, “Investigations on the Theory of Brownian Movement,” with notes by R. Furth, translated into English from German by A.D. Cowper, Methuen, London (1926), Dover Publications (1956).]Google Scholar
Feder, J. (1988). Fractals. New York, London: Plenum Press.
Kaye, B. (1989). A Random Walk through Fractal Dimensions. VCH Verlagsgsellschaft mbH. New York, Weinhein, Germany: VCH Publishers.
Ladaga, J.L & Bonetto, R.B. (2002). Characterisation of texture in scanning electron microscope images. In Advances in Imaging and Electron Physics, Hawkes, P.W. (Ed.), Vol. 120, pp. 136–189. San Diego, CA: Academic Press.
Lane, G.S. (1972). Dimensional measurements. In The Use of the Scanning Electron Microscope, Hearle, J.W.S., Sparrow, J.T. & Cross, P.M. (Eds.), pp. 219–238. New York: Pergamon Press.
Mandelbrot, B.B. (1982). The Fractal Geometry of Nature. New York: W.H. Freeman Co.
Mandelbrot, B.B., Passoja, D.E., & Paullay, A.J. (1984). Fractal character of fracture surfaces of metals. Nature 308, 721–722.Google Scholar
Ponz, E., Ladaga, J.L., & Bonetto, R.D. (2006). Measuring surface topography with scanning electron microscopy. I. EZEImage: A program to obtain 3D surface data. Microsc Microanal 12, 170–177 (this issue).Google Scholar
Russ, J.C. (1994). Fractal Surfaces. New York, London: Plenum Press.
Russ, J.C. (2002). The Image Processing Handbook, 4th ed. Florida: CRC Press, LLC.
Russ, J.C. & Russ, J.C. (1987). Feature-specific measurement of surface roughness in SEM images. Part Charact 4, 22–25.Google Scholar
Sayles, R.S. & Thomas, T.R. (1978). Surface topography as a nonstationary random process. Nature 271, 431–434.Google Scholar
Skands, U. (1996). Quantitative methods for the analysis of electron microscope images. Ph.D. Thesis, Technical University of Denmark, Institute of Mathematical Modelling, ISNN 0909-3192.
Sun, C. (2002). Fast stereo matching using rectangular subregioning and 3D maximum-surfaces techniques. Int J Comput Vision 47, 99–117.Google Scholar
Thomas, T.R., Rosén, B.G., & Amini, N. (1999). Fractal characterization of the anisotropy of rough surfaces. Wear 232, 41–50.Google Scholar
Van Put, A. (1991). Geochemical and morphological characterization of individual particles from the aqueous environment by EPXMA. Ph.D. Thesis, Universiteit Antwerpen, Universitaire Instelling Antwerpen, Departement Scheikunde, Belgium.